The present invention relates to an arithmetic unit, and more particularly to an FFT (Fast Fourier Transform) processing unit for performing FFT processing in response to input digital data successively supplied in serial form. FFT processing is, among other uses, utilized in the detection of particular frequency components in a speech signal analyzing system.
FFT processing is a high speed operation for performing with high efficiency DFT (Discrete Fourier Transform) processing, that is, an operation for detecting particular frequency components from a time series consisting of a number of sample values. This operation (FFT) is very frequently utilized in various communications and signal processing fields. One typical example of this operation can be seen in the analysis of speech signals in which after a speech signal has been sampled and subjected to analogue-digital conversion, particular frequency components involved in the speech signal can be detected by performing said DFT processing. Assuming here that the number of input data (sampled values of a speech waveform) used for DFT processing in N, N.sup.2 multiplications are needed to compute the DFT {X.sub.l } (l=0, 1, 2, . . . N-1) from the N-point input digital data series {x.sub.k } (k= 0, 1, 2, . . . N-1). FFT processing is employed as an arithmetic approach for greatly reducing the number of multiplications. General descriptions on DFT and FFT are given in detail in Chapter 6 of Digital Processing of Signals published in 1969 by McGraw-Hill Book Co., Inc. (Reference 1), and so, their detailed descriptions will be omitted.
In most cases, the aformentioned input digital data series {x.sub.k } are successively applied to an input terminal in serial form, and FFT processing upon this data series is performed for computation of {X.sub.l }. Heretofore, one conventional processing unit used in such a case has disadvantages in that its circuit structure and control operations are fairly complicated shown in FIG. 6 of an article titled "Digital Matched Filters Using Fast Fourier Transform" published in the Proceedings of EASCON on pages 222-230, 1971 (Reference 2).